A struggle for regular game time as part of a star-studded squad at Santiago Bernabeu has sparked exit talk surrounding the 22-year-old midfielder.
Premier League sides are reported to be keeping a close eye on his situation, with those at Old Trafford and Stamford Bridge prepared to open their doors to an exciting talent.
Asensio has, however, committed himself to Real, with the Spain international eager to point out that he joined the Blancos to make his mark on the grandest of stages.
A man who joined Madrid from Mallorca in 2014 and has won La Liga, the Champions League, UEFA Super Cup and two Club World Cups during his time at the Bernabeu said in a promotional video for Nike: "I always try with everything I have left.
"To reach the biggest club in the world where there are millions of fans and a lot of pressure was a brutal change. My debut was in a final. I was not nervous, I scored a goal and I won my first title.
"In all my debuts I've always been able to score goals and I have come to Madrid to stay and score many goals."
While he may not be a guaranteed starter for Real, Asensio has still enjoyed a productive 2017-18 season.
A 10-goal return has matched his efforts from last year’s double-winning campaign, with just one more effort required to set a new personal best.
He is determined to continue hitting targets such as that and raising the bar on a personal level, with Asensio stating when asked to describe himself in two words: "I have imagination and I am daring.”
Those qualities appear set to remain in Madrid, with any potential suitors having to turn their attention elsewhere.